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2-D Geometry Creation in PDE Modeler App

Create Basic Shapes

The PDE Modeler app lets you draw four basic shapes: a circle, an ellipse, a
rectangle, and a polygon. To draw a basic shape, use the Draw
menu or one of the following buttons on the toolbar. To cut, clear, copy, and paste the
solid objects, use the Edit menu.

Draw a rectangle/square starting at a corner.

Using
the left mouse button, drag to create a rectangle. Using the right
mouse button (or Ctrl+click), drag to create a
square.

Draw a rectangle/square starting at the center.

Using the left mouse button, drag to create a
rectangle. Using the right mouse button (or
Ctrl+click), drag to create a
square.

Draw an ellipse/circle starting at the perimeter.

Using the left mouse button, drag to create an ellipse.
Using the right mouse button (or Ctrl+click), drag
to create a circle.

Draw an ellipse/circle starting at the center.

Using the left mouse button, drag to create an ellipse.
Using the right mouse button (or Ctrl+click), drag
to create a circle.

Draw a polygon.

Using the left mouse button, drag
to create polygon edges. You can close the polygon by pressing the
right mouse button. Clicking at the starting vertex also closes the
polygon.

Alternatively, you can create a basic shape by typing one of the following commands in
the MATLAB® Command Window:

These commands open the PDE Modeler app with the requested shape already drawn in it.
If the app is already open, these commands add the requested shape to the app window
without deleting any existing shapes.

You can use a sequence of drawing commands to create several basic shapes. For
example, these commands create a circle, a rectangle, an ellipse, and a polygon:

Select Several Shapes

To select several shapes and to deselect shapes, use
Shift+click (or click using the middle mouse button). Clicking
outside of all shapes, deselects all shapes.

To select all the intersecting shapes, click the intersection of these
shapes.

To select all shapes, use the Select All option
from the Edit menu.

Rotate Shapes

To rotate a shape:

Select the shapes.

Select Rotate from the
Draw menu.

In the resulting Rotate dialog box, enter the rotation
angle in degrees. To rotate counterclockwise, use positive values of rotation
angles. To rotate clockwise, use negative values.

By default, the rotation center is the center-of-mass of the selected shapes.
To use a different rotation center, clear the Use
center-of-mass option and enter a rotation center
(xc,yc) as a 1-by-2 vector, for
example, [-0.4 0.3].

Create Complex Geometries

You can specify complex geometries by overlapping basic shapes. This approach is
called Constructive Solid Geometry (CSG). The PDE Modeler app lets you combine basic
shapes by using their unique names.

The app assigns a unique name to each shape. The names depend on the type of the
shape:

For circles, the default names are C1,
C2, C3, and so on.

For ellipses, the default names are E1,
E2, E3, and so on.

For polygons, the default names are P1,
P2, P3, and so on.

For rectangles, the default names are R1,
R2, R3, and so on.

For squares, the default names are SQ1,
SQ2, SQ3, and so on.

To change the name and parameters of a shape, first switch to the draw mode and then
double-click the shape. (Select Draw Mode from the
Draw menu to switch to the draw mode.) The resulting
dialog box lets you change the name and parameters of the selected shape. The name
cannot contain spaces.

Now you can combine basic shapes to create a complex geometry. To do this, use the
Set formula field located under the toolbar. Here you can
specify a geometry by using the names of basic shapes and the following
operators:

+ is the set union operator.

For example, SQ1+C2 creates a geometry comprised of all
points of the square SQ1 and all points of the circle
C2.

* is the set intersection operator.

For example, SQ1*C2 creates a geometry comprised of the
points that belong to both the square SQ1 and the circle
C2.

- is the set difference operator.

For example, SQ1-C2 creates a geometry comprised of the
points of the square SQ1 that do not belong to the circle
C2.

The operators + and * have the same precedence.
The operator - has a higher precedence. You can control the
precedence by using parentheses. The resulting geometrical model (called
decomposed geometry) is the set of points for which the set
formula evaluates to true. By default, it is the union of all basic shapes.

Adjust Axes Limits and Grid

To adjust axes limits:

Select Axes Limits from the
Options menu

Specify the range of the x-axis and the
y-axis as a 1-by-2 vector such as [-10
10]. If you select Auto, the app uses
automatic scaling for the corresponding axis.

Apply the specified axes ranges by clicking
Apply.

Close the dialog box by clicking Close.

To add axis grid, the snap-to-grid feature, and zoom, use the
Options menu. To adjust the grid spacing:

Specify the grid spacing for the x-axis and
y-axis. For example, change the default linear spacing
-1.5:0.5:1.5 to -1:0.2:1.

You also can add extra ticks to customize the grid and aid in drawing. To
separate extra tick entries, use spaces, commas, semicolons, or brackets.

Apply the specified grid spacing by clicking
Apply.

Close the dialog box by clicking Done.

Create Geometry with Rounded Corners

Open the PDE Modeler app by using the pdeModeler
command.

Display grid lines by selecting Options > Grid.

Align new shapes to the grid lines by selecting Options > Snap.

Set the grid spacing for x-axis to
-1.5:0.1:1.5 and for y-axis to
-1:0.1:1. To do this, select Options > Grid Spacing, clear the Auto checkboxes, and set the
corresponding ranges.

Draw a rectangle with the width 2, the height 1, and the top left corner at
(–1,0.5). To do this, first click the button. Then click the point (–1,0.5) and drag to draw a
rectangle.

To edit the parameters of the rectangle, double-click it. In the resulting
dialog box, specify the exact parameters.

Draw four circles with the radius 0.2 and the centers at (–0.8,–0.3),
(–0.8,0.3), (0.8,–0.3), and (0.8,0.3).To do this, first click the button. Then click the center of a circle using the right
mouse button and drag to draw a circle. The right mouse button constrains the
shape you draw to be a circle rather than an ellipse. If the circle is not a
perfect unit circle, then double-click it. In the resulting dialog box, specify
the exact center location and radius of the circle.

Add four squares with the side 0.2, one in each corner.

Model the geometry with rounded corners by subtracting the small squares from
the rectangle, and then adding the circles. To do this, enter the following
formula in the Set formula field.

R1-(SQ1+SQ2+SQ3+SQ4)+C1+C2+C3+C4

Switch to the boundary mode by clicking the button or selecting Boundary > Boundary Mode. The CSG model is now decomposed using the set formula, and you
get a rectangle with rounded corners.

Because of the intersection of the solid objects used in the initial CSG
model, a number of subdomain borders remain. They appear as gray lines. To
remove these borders, select Boundary > Remove All Subdomain Borders.

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